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          <h1 class="post-title" itemprop="name headline">PAT A1087</h1>
        

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        <p>Indeed there are many different tourist routes from our city to Rome. You are supposed to find your clients the route with the least cost while gaining the most happiness.</p>
<p>Input Specification:</p>
<p>Each input file contains one test case. For each case, the first line contains 2 positive integers N (2&lt;=N&lt;=200), the number of cities, and K, the total number of routes between pairs of cities; followed by the name of the starting city. The next N-1 lines each gives the name of a city and an integer that represents the happiness one can gain from that city, except the starting city. Then K lines follow, each describes a route between two cities in the format “City1 City2 Cost”. Here the name of a city is a string of 3 capital English letters, and the destination is always ROM which represents Rome.</p>
<p>Output Specification:</p>
<p>For each test case, we are supposed to find the route with the least cost. If such a route is not unique, the one with the maximum happiness will be recommended. If such a route is still not unique, then we output the one with the maximum average happiness – it is guaranteed by the judge that such a solution exists and is unique.</p>
<p>Hence in the first line of output, you must print 4 numbers: the number of different routes with the least cost, the cost, the happiness, and the average happiness (take the integer part only) of the recommended route. Then in the next line, you are supposed to print the route in the format “City1-&gt;City2-&gt;…-&gt;ROM”.</p>
<p>Sample Input:<br>6 7 HZH<br>ROM 100<br>PKN 40<br>GDN 55<br>PRS 95<br>BLN 80<br>ROM GDN 1<br>BLN ROM 1<br>HZH PKN 1<br>PRS ROM 2<br>BLN HZH 2<br>PKN GDN 1<br>HZH PRS 1<br>Sample Output:<br>3 3 195 97<br>HZH-&gt;PRS-&gt;ROM</p>
<p>仅用dijstra：<br><figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br></pre></td><td class="code"><pre><span class="line">#include &quot;stdio.h&quot;</span><br><span class="line">#include &quot;math.h&quot;</span><br><span class="line">#include &quot;string.h&quot;</span><br><span class="line">#include &quot;iostream&quot;</span><br><span class="line">//#include &quot;stdlib.h&quot;</span><br><span class="line">#include &quot;vector&quot;</span><br><span class="line">#include &quot;set&quot;</span><br><span class="line">#include &quot;map&quot;</span><br><span class="line">//#include &quot;stack&quot;</span><br><span class="line">#include &quot;queue&quot;</span><br><span class="line">#include &quot;algorithm&quot;</span><br><span class="line">using namespace std;</span><br><span class="line"></span><br><span class="line">const int MAXV = 410;//最大顶点数</span><br><span class="line">const int INF = 1000000000;//无穷大</span><br><span class="line">//n 城市数目, k 边数, G 邻接矩阵, w 点权</span><br><span class="line">//d[]最短距离,dw[]最大点权,num[]最短路径条数</span><br><span class="line">//pt[]记录最短路径上的顶点数,pre[]记录前驱</span><br><span class="line">int n, k, G[MAXV][MAXV], weight[MAXV];</span><br><span class="line">int d[MAXV], w[MAXV], num[MAXV], pt[MAXV], pre[MAXV];</span><br><span class="line">bool vis[MAXV] = &#123;false&#125;;</span><br><span class="line">map&lt;string, int&gt; cityToIndex;</span><br><span class="line">map&lt;int, string&gt; indexToCity;</span><br><span class="line"></span><br><span class="line">void Dijkstra(int s)&#123;</span><br><span class="line">    fill(d, d + MAXV, INF);</span><br><span class="line">    memset(w, 0, sizeof(w));</span><br><span class="line">    memset(num, 0, sizeof(num));</span><br><span class="line">    memset(pt, 0, sizeof(pt));</span><br><span class="line">    for (int i = 0; i &lt; n; i++) pre[i] = i;//前驱初始化</span><br><span class="line">    d[s] = 0;</span><br><span class="line">    w[s] = 0;</span><br><span class="line">    num[s] = 1;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;//循环n次</span><br><span class="line">        int u = -1, MIN = INF;</span><br><span class="line">        for (int j = 0; j &lt; n; j++) &#123;</span><br><span class="line">            if (vis[j] == false &amp;&amp; d[j] &lt; MIN) &#123;</span><br><span class="line">                u = j;</span><br><span class="line">                MIN = d[j];</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        if (u == -1) return;</span><br><span class="line">        vis[u] = true;</span><br><span class="line">        for (int v = 0; v &lt; n; v++) &#123;</span><br><span class="line">            if (vis[v] == false &amp;&amp; G[u][v] != INF) &#123;</span><br><span class="line">                if (d[u] + G[u][v] &lt; d[v]) &#123;</span><br><span class="line">                    d[v] = d[u] + G[u][v];//优化d[v]</span><br><span class="line">                    w[v] = w[u] + weight[v];</span><br><span class="line">                    num[v] = num[u];</span><br><span class="line">                    pt[v] = pt[u] + 1;</span><br><span class="line">                    pre[v] = u;</span><br><span class="line">                &#125;else if (d[u] + G[u][v] == d[v])&#123;</span><br><span class="line">                    num[v] += num[u];//加最短路径条数</span><br><span class="line">                    if (w[u] + weight[v] &gt; w[v]) &#123;</span><br><span class="line">                        w[v] = w[u] + weight[v];</span><br><span class="line">                        pt[v] = pt[u] + 1;</span><br><span class="line">                        pre[v] = u;</span><br><span class="line">                    &#125;else if(w[u] + weight[v] == w[v])&#123;</span><br><span class="line">                        double uAvg = 1.0 * (w[u] + weight[v]) / (pt[u] + 1);</span><br><span class="line">                        double vAvg = 1.0 * w[v] / pt[v];</span><br><span class="line">                        if (uAvg &gt; vAvg) &#123;</span><br><span class="line">                            pt[v] = pt[u] + 1;</span><br><span class="line">                            pre[v] = u;</span><br><span class="line">                        &#125;</span><br><span class="line">                    &#125;</span><br><span class="line">                &#125;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line">void printPath(int v)&#123;</span><br><span class="line">    if (v == 0) &#123;</span><br><span class="line">        cout &lt;&lt; indexToCity[v];</span><br><span class="line">        return;</span><br><span class="line">    &#125;</span><br><span class="line">    printPath(pre[v]);</span><br><span class="line">    cout &lt;&lt;&quot;-&gt;&quot;&lt;&lt;indexToCity[v];</span><br><span class="line">&#125;</span><br><span class="line">int main()&#123;</span><br><span class="line">    string start, str1, str2;</span><br><span class="line">    cin &gt;&gt; n &gt;&gt; k &gt;&gt; start;</span><br><span class="line">    cityToIndex[start] = 0;</span><br><span class="line">    indexToCity[0] = start;</span><br><span class="line">    for (int i = 1; i &lt;= n - 1; i++) &#123;</span><br><span class="line">        cin &gt;&gt; str1 &gt;&gt; weight[i];//读入happy值，点权</span><br><span class="line">        cityToIndex[str1] = i;</span><br><span class="line">        indexToCity[i] = str1;</span><br><span class="line">    &#125;</span><br><span class="line">    fill(G[0], G[0] + MAXV * MAXV, INF);//初始化图G</span><br><span class="line">    for (int i = 0; i &lt; k; i++)&#123;</span><br><span class="line">        cin &gt;&gt; str1 &gt;&gt; str2;</span><br><span class="line">        int c1 = cityToIndex[str1], c2 = cityToIndex[str2];</span><br><span class="line">        cin &gt;&gt; G[c1][c2];</span><br><span class="line">        G[c2][c1] = G[c1][c2];//无向边</span><br><span class="line">    &#125;</span><br><span class="line">    Dijkstra(0);</span><br><span class="line">    int rom = cityToIndex[&quot;ROM&quot;];</span><br><span class="line">    printf(&quot;%d %d %d %d\n&quot;, num[rom], d[rom], w[rom], w[rom]/pt[rom]);</span><br><span class="line">    printPath(rom);</span><br><span class="line">    return 0;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></p>
<p>dijstra + dfs:<br><figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br></pre></td><td class="code"><pre><span class="line">#include &quot;stdio.h&quot;</span><br><span class="line">#include &quot;math.h&quot;</span><br><span class="line">#include &quot;string.h&quot;</span><br><span class="line">#include &quot;iostream&quot;</span><br><span class="line">//#include &quot;stdlib.h&quot;</span><br><span class="line">#include &quot;vector&quot;</span><br><span class="line">#include &quot;set&quot;</span><br><span class="line">#include &quot;map&quot;</span><br><span class="line">//#include &quot;stack&quot;</span><br><span class="line">#include &quot;queue&quot;</span><br><span class="line">#include &quot;algorithm&quot;</span><br><span class="line">using namespace std;</span><br><span class="line"></span><br><span class="line">const int MAXV = 410;//最大顶点数</span><br><span class="line">const int INF = 1000000000;//无穷大</span><br><span class="line">//n 城市数目, k 边数, G 邻接矩阵, w 点权</span><br><span class="line">//d[]最短距离,numPath记录最短路径条数</span><br><span class="line">//maxW记录最大点权之和，maxAvg为最大平均点权</span><br><span class="line">int n, k, G[MAXV][MAXV], weight[MAXV];</span><br><span class="line">int d[MAXV], numPath = 0, maxW = 0;</span><br><span class="line">double maxAvg = 0;</span><br><span class="line">bool vis[MAXV] = &#123;false&#125;;</span><br><span class="line">vector&lt;int&gt; pre[MAXV];</span><br><span class="line">vector&lt;int&gt; tempPath, path;</span><br><span class="line">map&lt;string, int&gt; cityToIndex;</span><br><span class="line">map&lt;int, string&gt; indexToCity;</span><br><span class="line"></span><br><span class="line">void Dijstra(int s)&#123;//起点s</span><br><span class="line">    fill(d, d + MAXV, INF);</span><br><span class="line">    d[s] = 0;</span><br><span class="line">    for (int i = 0; i &lt; n; i++) &#123;</span><br><span class="line">        int u = -1, MIN = INF;</span><br><span class="line">        for (int j = 0; j &lt; n; j++) &#123;</span><br><span class="line">            if (vis[j] == false &amp;&amp; d[j] &lt; MIN) &#123;</span><br><span class="line">                u = j;</span><br><span class="line">                MIN = d[j];</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        if (u == -1) return;</span><br><span class="line">        vis[u] = true;</span><br><span class="line">        for (int v = 0; v &lt; n; v++) &#123;</span><br><span class="line">            if (vis[v] == false &amp;&amp; G[u][v] != INF) &#123;</span><br><span class="line">                if (d[u] + G[u][v] &lt; d[v]) &#123;</span><br><span class="line">                    d[v] = d[u] + G[u][v];</span><br><span class="line">                    pre[v].clear();</span><br><span class="line">                    pre[v].push_back(u);</span><br><span class="line">                &#125; else if(d[u] + G[u][v] == d[v])&#123;</span><br><span class="line">                    pre[v].push_back(u);</span><br><span class="line">                &#125;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line">void DFS(int v)&#123;</span><br><span class="line">    if (v == 0) &#123;</span><br><span class="line">        tempPath.push_back(v);</span><br><span class="line">        numPath++;</span><br><span class="line">        int tempW = 0;//临时路径tempPath的点权之和</span><br><span class="line">        for (int i = tempPath.size() - 2; i &gt;= 0; i--) &#123;</span><br><span class="line">            int id = tempPath[i];</span><br><span class="line">            tempW += weight[id];</span><br><span class="line">        &#125;</span><br><span class="line">        double tempAvg = 1.0 * tempW / (tempPath.size() - 1);</span><br><span class="line">        if (tempW &gt; maxW) &#123;//当前点权和更大</span><br><span class="line">            maxW = tempW;</span><br><span class="line">            maxAvg = tempAvg;</span><br><span class="line">            path = tempPath;</span><br><span class="line">        &#125;else if (tempW == maxAvg &amp;&amp; tempAvg &gt; maxAvg)&#123;</span><br><span class="line">            maxAvg = tempAvg;</span><br><span class="line">            path = tempPath;</span><br><span class="line">        &#125;</span><br><span class="line">        tempPath.pop_back();</span><br><span class="line">        return;</span><br><span class="line">    &#125;</span><br><span class="line">    tempPath.push_back(v);</span><br><span class="line">    for (int i = 0; i &lt; pre[v].size(); i++) &#123;</span><br><span class="line">        DFS(pre[v][i]);</span><br><span class="line">    &#125;</span><br><span class="line">    tempPath.pop_back();</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line">int main()&#123;</span><br><span class="line">    string start, city1, city2;</span><br><span class="line">    cin &gt;&gt; n &gt;&gt; k &gt;&gt; start;</span><br><span class="line">    cityToIndex[start] = 0;</span><br><span class="line">    indexToCity[0] = start;</span><br><span class="line">    for (int i = 1; i &lt;= n -1; i++) &#123;</span><br><span class="line">        cin &gt;&gt; city1 &gt;&gt; weight[i];</span><br><span class="line">        cityToIndex[city1] = i;</span><br><span class="line">        indexToCity[i] = city1;</span><br><span class="line">    &#125;</span><br><span class="line">    fill(G[0], G[0] + MAXV * MAXV, INF);</span><br><span class="line">    for (int i = 0; i &lt; k; i++) &#123;</span><br><span class="line">        cin &gt;&gt; city1 &gt;&gt; city2;</span><br><span class="line">        int c1 = cityToIndex[city1], c2 = cityToIndex[city2];</span><br><span class="line">        cin &gt;&gt; G[c1][c2];</span><br><span class="line">        G[c2][c1] = G[c1][c2];</span><br><span class="line">    &#125;</span><br><span class="line">    Dijstra(0);</span><br><span class="line">    int rom = cityToIndex[&quot;ROM&quot;];</span><br><span class="line">    DFS(rom);</span><br><span class="line">    printf(&quot;%d %d %d %d\n&quot;, numPath, d[rom], maxW, (int)maxAvg);</span><br><span class="line">    for (int i = path.size() - 1; i &gt;= 0; i--) &#123;</span><br><span class="line">        cout &lt;&lt; indexToCity[path[i]];</span><br><span class="line">        if (i &gt; 0) &#123;</span><br><span class="line">            cout &lt;&lt;&quot;-&gt;&quot;;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    return 0;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></p>

      
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